Log24

Friday, April 21, 2017

Music Box

Filed under: Uncategorized — Tags: — m759 @ 3:07 PM

Guitart et al. on 'box' theory of creativity

A box from the annus mirabilis

See Hudson's 4×4 array.

Related material —

Thursday, April 20, 2017

Stone Logic

Filed under: Uncategorized — m759 @ 9:48 PM

See also "Romancing the Omega" —

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Related mathematics — Guitart in this journal —

From 'Moving Logic, from Boole to Galois,' by René Guitart, 2005

See also Weyl + Palermo in this journal —

http://www.log24.com/log/pix11B/110922-TriquetrumCube.jpg

Monday, August 22, 2016

Minimal ABC Art

Filed under: Uncategorized — Tags: — m759 @ 7:00 PM

Two portions of a post from Guy Fawkes Day 2015

 

Other art for Guy Fawkes Day

Cloak and Dagger

Saturday, May 21, 2016

Fitzgerald and Paris

Filed under: Uncategorized — m759 @ 10:08 AM

The previous post suggests two images

The date of the above Promoted Tweet is October 19, 2015.

For the Church of Synchronology, an image from Log24 on that date:

"So we beat on, boats against the current " — F. Scott Fitzgerald

Monday, May 2, 2016

Quality

Filed under: Uncategorized — Tags: — m759 @ 3:48 PM

The previous post, on subjective  and objective  quality,
suggests a review of Pirsig

     "And finally: Phaedrus, following a path
that to his knowledge had never been taken before
in the history of Western thought,
went straight between the horns of
the subjectivity-objectivity dilemma and said
Quality is neither a part of mind, nor is it a part of matter.
It is a third  entity which is independent of the two.
     He was heard along the corridors
and up and down the stairs of Montana Hall
singing softly to himself, almost under his breath,
'Holy, holy, holy…blessed Trinity.' "

See also Guitart in this journal, noting esp. Zen and the Art.

Wednesday, April 20, 2016

Symmetric Generation of a Simple Group

Filed under: Uncategorized — m759 @ 9:00 PM

The reference in the previous post to the work of Guitart and 
The Road to Universal Logic  suggests a fiction involving
the symmetric generation of the simple group of order 168.

See The Diamond Archetype and a fictional account of the road to Hell 

'PyrE' in Bester's 'The Stars My Destination'

The cover illustration below has been adapted to
replace the flames of PyrE with the eightfold cube.

IMAGE- 'The Stars My Destination' (with cover slightly changed)

For related symmetric generation of a much larger group, see Solomon's Cube.

Detour …

Filed under: Uncategorized — m759 @ 2:00 PM

on the Road to Universal Logic

Deck the Halls.

Thursday, November 5, 2015

ABC Art or: Guitart Solo

Filed under: Uncategorized — Tags: — m759 @ 5:55 PM

"… the A B C of being…." — Wallace Stevens

Scholia —

Compare to my own later note, from March 4, 2010 —

"It seems that Guitart discovered these 'A, B, C' generators first,
though he did not display them in their natural setting,
the eightfold cube." — Borromean Generators (Log24, Oct. 19)

See also Raiders of the Lost Crucible (Halloween 2015)
and "Guitar Solo" from the 2015 CMA Awards on ABC.

Wednesday, October 21, 2015

Priest Logic for Frodo

Filed under: Uncategorized — m759 @ 12:00 AM

Elijah Wood in "The Last Witch Hunter" —

See Graham Priest in this journal.

See also Coxeter + Discursive.

Tuesday, October 20, 2015

Liminal

Filed under: Uncategorized — m759 @ 3:33 PM

The New York Times  has a readable, if not informative,
review of a recent controversial account of history —

"For many, it exists in a kind of liminal state,
floating somewhere between fact and mythology."

Jonathan Mahler, online Times  on Oct. 15, 2015

[See Wikipedia on Liminality.]

Mahler begins his review with a statement by the President
on the night of May 1, 2011.

A more easily checked statement quoted here  on that date:

"The positional meaning of a symbol derives from
its relationship to other symbols in a totality, a Gestalt,
whose elements acquire their significance from the
system as a whole."

— Victor Turner, The Forest of Symbols , Ithaca, NY,
Cornell University Press, 1967, p. 51, quoted by
Beth Barrie in "Victor Turner."

A Gestalt  from "Verhexung ," the previous post —

Guitart's statement that the above figure is a "Boolean logical cube"
seems, in the words of the Times , to be "floating somewhere
between fact and mythology."  Discuss.

(My apologies to those who feel that attempting to make sense
of Guitart makes them feel like Vin Diesel in the Dreamworld.)

Verhexung

Filed under: Uncategorized — m759 @ 5:04 AM

"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."

— Philosophical Investigations  (1953),  Section 109

An example of Verhexung  from the René Guitart article in the previous post

See also Ein Kampf .

Monday, October 19, 2015

Symmetric Generation of the Simple Order-168 Group

Filed under: Uncategorized — m759 @ 8:48 PM

This post continues recent thoughts on the work of René Guitart.  
A 2014 article by Guitart gives a great deal of detail on his
approach to symmetric generation of the simple group of order 168 —

"Hexagonal Logic of the Field F8 as a Boolean Logic
with Three Involutive Modalities," pp. 191-220 in

The Road to Universal Logic:
Festschrift for 50th Birthday of
Jean-Yves Béziau, Volume I,

Editors: Arnold Koslow, Arthur Buchsbaum,
Birkhäuser Studies in Universal Logic, dated 2015
by publisher but Oct. 11, 2014, by Amazon.com.

See also the eightfold cube in this journal.

Zen and the Art

Filed under: Uncategorized — m759 @ 4:40 AM

According to René Guitart in May 2008 —

"In fact, in concrete terms, the Mathematical Pulsation  is
nothing else but the thing that everyone does when doing
mathematics, even the most elementary ones. It is a very
special gesture in understanding ('geste de pensée'), well
known by each mathematician. The mind have to go to
and fro between to antinomical postures: to have the
situation under control, to leave the door open. To master
and to fix (a clear unique meaning) or to neglect and to
change (toward other possible meanings). Because of the
similarity of the pulsation of inspiration and expiration in
breath with the pulsation of closing and opening phases
in mathematical thinking, at the end of [Guitart (2003/a)]
I suggested to consider the famous book 'Zen in the Art
of Archery' [Herrigel (1997)] as a true treatise in didactic
of mathematics: just you have to replace everywhere the
words 'archery' by 'mathematical proof'."

Related material: Heisenberg on Beauty and the previous post.

Update of 6:20 AM Oct. 19, 2015 —

„Ich begriff plötzlich, daß in der Sprache oder doch
mindestens im Geist des Glasperlenspiels tatsächlich
alles allbedeutend sei, daß jedes Symbol und jede
Kombination von Symbolen nicht hierhin oder dorthin,
nicht zu einzelnen Beispielen, Experimenten und
Beweisen führe, sondern ins Zentrum, ins Geheimnis
und Innerste der Welt, in das Urwissen. Jeder Übergang
von Dur zu Moll in einer Sonate, jede Wandlung eines
Mythos oder eines Kultes, jede klassische, künstlerische
Formulierung sei, so erkannte ich im Blitz jenes
Augenblicks, bei echter meditativer Betrachtung,
nichts andres als ein unmittelbarer Weg ins Innere
des Weltgeheimnisses, wo im Hin und Wider zwischen
Ein- und Ausatmen, zwischen Himmel und Erde,
zwischen Yin und Yang sich ewig das Heilige vollzieht.“

— Hermann Hesse, Das Glasperlenspiel.
Berlin:  Suhrkamp Taschenbuch Verlag, 2012. p. 172,
as quoted in a weblog.

For a version in English, see Summa Mythologica (Nov. 3, 2009).

Borromean Generators

Filed under: Uncategorized — Tags: — m759 @ 4:10 AM

From slides dated June 28, 2008

Compare to my own later note, from March 4, 2010 —

It seems that Guitart discovered these "A, B, C" generators first,
though he did not display them in their natural setting,
the eightfold cube.

Some context: The epigraph to my webpage
"A Simple Reflection Group of Order 168" —

"Let G  be a finite, primitive subgroup of GL(V) = GL(n,D) ,
where  is an n-dimensional vector space over the
division ring D . Assume that G  is generated by 'nice'
transformations. The problem is then to try to determine
(up to GL(V) -conjugacy) all possibilities for G . Of course,
this problem is very vague. But it is a classical one,
going back 150 years, and yet very much alive today."

— William M. Kantor, "Generation of Linear Groups,"
pp. 497-509 in The Geometric Vein: The Coxeter Festschrift ,
published by Springer, 1981 

Saturday, September 5, 2015

For the Machiavelli School*

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

See also Weyl + Palermo in this  journal —

http://www.log24.com/log/pix11B/110922-TriquetrumCube.jpg

* The title refers to the previous post, on a current New Yorker  cartoon.

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